An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

Thanks to a rapid progress of high-power lasers since the birth of laser by T. H. Maiman in 1960, intense lasers have been developed mainly for studying the scientific feasibility of laser fusion. Inertial confinement fusion with an intense laser has attracted attention as a new future energy source after two oil crises in the 1970s and 1980s. From the beginning, the most challenging physics is known to be the hydrodynamic instability to realize the spherical implosion to achieve more than 1000 times the solid density. Many studies have been performed theoretically and experimentally on the hydrodynamic instability and resultant turbulent mixing of compressible fluids. During such activities in the laboratory, the explosion of supernova SN1987A was observed in the sky on 23 February 1987. The X-ray satellites have revealed that the hydrodynamic instability is a key issue to understand the physics of supernova explosion. After collaboration between laser plasma researchers and astrophysicists, the laboratory astrophysics with intense lasers was proposed and promoted around the end of the 1990s. The original subject was mainly related to hydrodynamic instabilities. However, after two decades of laboratory astrophysics research, we can now find a diversity of research topics. It has been demonstrated theoretically and experimentally that a variety of nonlinear physics of collisionless plasmas can be studied in laser ablation plasmas in the last decade. In the present paper, we shed light on the recent 10 topics studied intensively in laboratory experiments. A brief review is given by citing recent papers. Then, modeling cosmic-ray acceleration with lasers is reviewed in a following session as a special topic to be the future main topic in laboratory astrophysics research.

The process of high energy electron acceleration along the surface of grating targets (GTs) that were irradiated by a relativistic, high-contrast laser pulse at an intensity $I=2.5\times 10^{20}~\text{W}/\text{cm}^{2}$ was studied. Our experimental results demonstrate that for a GT with a periodicity twice the laser wavelength, the surface electron flux is more intense for a laser incidence angle that is larger compared to the resonance angle predicted by the linear model. An electron beam with a peak charge of ${\sim}2.7~\text{nC}/\text{sr}$, for electrons with energies ${>}1.5~\text{MeV}$, was measured. Numerical simulations carried out with parameters similar to the experimental conditions also show an enhanced electron flux at higher incidence angles depending on the preplasma scale length. A theoretical model that includes ponderomotive effects with more realistic initial preplasma conditions suggests that the laser-driven intensity and preformed plasma scale length are important for the acceleration process. The predictions closely match the experimental and computational results.

With the latest configuration, the Ti:Sa laser system ARCTURUS (Düsseldorf University, Germany) operates with a double-chirped pulse amplification (CPA) architecture delivering pulses with an energy of 7 J before compression in each of the two high-power beams. By the implementation of a plasma mirror system, the intrinsic laser contrast is enhanced up to $10^{-12}$ on a time scale of hundreds of picoseconds, before the main peak. The laser system has been used in various configurations for advanced experiments and different studies have been carried out employing the high-power laser beams as a single, high-intensity interaction beam ($I\approx 10^{20}~\text{W}/\text{cm}^{2}$), in dual- and multi-beam configurations or in a pump–probe arrangement.

Propagation effects on radio emission within the pulsar magnetosphere are discussed. Widely accepted pulsar models assume that a pulsar magnetosphere is populated with relativistic pair plasmas produced through electron–positron cascades by accelerated primary particles above the polar cap. Any radio emission produced well inside the light cylinder (the radius at which the rotation speed equals c) must propagate through the magnetospheric plasma and be subject to plasma dispersion effects such as refraction and absorption. The observed pulse profiles should contain some features that reflect the influence of the intervening plasma. I discuss particularly the absorption effect due to cyclotron resonance and its possible observational consequences.

We present the temporal and spatial characterization of X-ray sources (at ~1 keV) driven by a 200 TW, 30 fs, 800 nm laser pulse on SILEX-I laser facility at Research Center of Laser Fusion. For laser copper foil interaction with laser intensity between 6 × 1018 W/cm2 and 3 × 1019 W/cm2, the X-ray images show cone-like jet structures. While the yield of X-rays is strongly dependent on the laser intensity, the plasma expansion length is weakly dependent on the laser intensity, and the open angle of the cone-like jet is not correlated to the laser intensity. The formation of the jet structure is attributed to the plasma transverse confine by the self-induced quasi-static magnetic field. An X-ray pedestal 4 ns preceding the main pulse was observed. The correlation between X-ray pedestal and collimated proton beam generation was found.

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.